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JEE Main & Advanced Mathematics Binomial Theorem and Mathematical Induction Question Bank General term, Coefficient of any power of x, Independent term, Middle term and Greatest term and Greatest coefficient

  • question_answer
    The coefficient of \[{{x}^{7}}\] in the expansion of \[{{\left( \frac{{{x}^{2}}}{2}-\frac{2}{x} \right)}^{8}}\] is [MNR 1975]

    A) - 56

    B) 56

    C) - 14

    D) 14

    Correct Answer: C

    Solution :

      \[(8-r)(2)+r(-1)=7\Rightarrow 16-2r-r=7\Rightarrow r=3\] Thus coefficient of x7 is \[={{\,}^{8}}{{C}_{3}}{{\left( \frac{1}{2} \right)}^{5}}{{(-2)}^{3}}=-\frac{8\times 7\times 6}{3\times 2\times 1}\times \frac{1}{4}=-14\].


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